Surface Lattice Dynamics of Silver. I. Low-Energy Electron Debye-Waller Factor

Abstract

We have investigated the temperature dependence of the low-energy electron diffraction from the (111) surface of silver between 300 and 600°K using an apparatus containing a two-circle goniometer and provision for both visual display of the diffraction pattern and the more precise measurement of the diffracted current with a moveable Faraday cage. The penetration of the electrons is estimated from the energy dependence of the diffracted intensity and is shown to be described by an absorption coefficient which is approximately proportional to $E^{-\frac{1}{2}}$ for energies above 120 eV. Below 120 eV the penetration is a steeper function of energy. Measurements of the effective Debye temperature ${\Theta }^{\prime }$ for various angles of incidence corroborate the functional dependence of the penetration of energy. From a knowledge of ${\Theta }^{\prime }$ and the penetration, we estimate the mean square thermal displacements normal to the crystal surface as a function of depth. At the surface these displacements are 2.0±0.2 times larger than in the bulk, and the amplitude approaches the bulk value nearly as $e^{-n}$, where $n$ labels the plane. These results agree with recent model calculations. Measurements of the thermal displacements in other directions indicate that the excess amplitude is nearly isotropic, in disagreement with the model calculations.